Program to find partition array into disjoint intervals in Python

Suppose we have an array nums, we have to partition it into two different subarrays called left and right such that −

• Each element in left subarray is less than or equal to each element in right subarray.

• left and right subarrays are non-empty.

• left subarray has the smallest possible size.

We have to find the length of left after such a partitioning.

So, if the input is like nums = [5,0,3,8,6], then the output will be 3 because left array will be [5,0,3] and right subarray will be [8,6].

To solve this, we will follow these steps −

• mx := null, temp := null, nmx := null

• temp2 := 0

• for each i in nums, do

  • if mx is same as null, then

    • mx := i

    • nmx := i

    • temp := temp2

    • temp2 := temp2 + 1

    • go for next iteration

  • if i>=mx, then

    • temp2 := temp2 + 1

    • if i>nmx, then

      • nmx := i

    • go for next iteration

  • otherwise,

    • temp := temp2

    • temp2 := temp2 + 1

    • mx := nmx

    • go for next iteration

• return temp+1

Example

Let us see the following implementation to get better understanding −

def solve(nums):
   mx = None
   temp = None
   nmx = None
   temp2 = 0

   for i in nums:

      if(mx==None):
         mx = i
         nmx = i
         temp = temp2
         temp2+=1
         continue

      if(i>=mx):
         temp2+=1
         if(i>nmx):
            nmx = i
         continue

      else:
         temp = temp2
         temp2+=1
         mx = nmx
         continue

   return temp+1

nums = [5,0,3,8,6]
print(solve(nums))

Input

[5,0,3,8,6]

Output

3